The run test for the large sample sizes

If the sample size is large , the distribution of the runs under the null hypothesis can be approximated by a normal distribution. Under the null hypothesis the random variable

has a standard normal distribution. In formula above, defines the number of runs, as the number of sequences above or below the median.

We want to test the null hypothesis

The series is random

1) If the alternative hypothesis is positive association between adjacent observations, the decision rule is

Reject if

2) If the alternative hypothesis is that series are nonrandom, then the decision rule is

Reject if or

Remark:

To use MINITAB menu follow the following instructions

1. Select Stat>Nonparametrics>Runs test

2. Enter time series variable (for example, C1)

3. Select

4. Insert value of the median

5. Select “generate forecasts”

6. Click OK.

Дата добавления: 2015-08-05